## Uniqueness clue cover

Advanced methods and approaches for solving Sudoku puzzles

### Uniqueness clue cover

Hi !
I am "puzzled" by the following puzzle from Mauricio (source: Sudopedia on "uniqueness clue cover")
Code: Select all
`*-----------*|...|...|...||...|...|..2||...|..1|...||---+---+---||..1|.3.|.4.||..5|6.7|3..||.3.|.2.|..8||---+---+---||..2|.6.|5..||65.|..8|9.4||9..|4..|..7|*-----------*`

.................2.....1.....1.3..4...56.73...3..2...8..2.6.5..65...89.49..4....7 ER = 8.4
Following the very short explanation given at the sudopedia site, one can make r1c9=1, solving the puzzle with singles.
From that site:
More dramatically, if a band contains just two clues in the arrangement shown (starred) below, then all of the unclued values are eliminated from two other cells. Note that although it is obvious that -@ in r2c3 implies r2c3=1, this placement is not shown because the elimination of 2 from r2c3 does not require any uniqueness assumption: we are applying the definition strictly.
Code: Select all
`+-------------+-------------+-------------+|   .   .   . |   .   .   . |   .   .  *1 ||   .   .  -@ |   .   .   . |   .   .  -@ ||   .   .  *2 |   .   .   . |   .   .   . |+-------------+-------------+-------------+`

These eliminations are available because only a few special types of band (in this case) can be covered by just two clues in any proper, single-solution, puzzle. Knowing the form that these special band types take, by computer searching, allows us to make the eliminations shown.

I may have misunderstood something. Is there (nowadays) a way (proof) to justify that placement using uniqueness but without "computer searching" ? I could not find a thread on this and Wecoc's List of Acronyms points only to Sudopedia.

JCO
jco

Posts: 551
Joined: 09 June 2020

### Re: Uniqueness clue cover

If i remember right:
As it says above, all possible solution grids for puzzles with only 2 clues given in a band in different boxes and rows, do have this property (the band alone of course can have many other solutions, but for a unique puzzle solution without that property you would need another given in the band). That was found by exhaustive search.
But i cannot find a reference, when/where that was shown.
eleven

Posts: 2976
Joined: 10 February 2008

### Re: Uniqueness clue cover

reverse bug
by ruud

if i remember correctly covered the early proof and "UCC" yiddish version of "yuck" exhaustively searched unavoidable sets for reduced space to prove it somewhere just as we lost the original server.
Some do, some teach, the rest look it up.
stormdoku

StrmCkr

Posts: 1336
Joined: 05 September 2006